bootstrap2x2

Description

Parametric Bootstrap of 2x2 Contingence independence test. The goodness of fit statistic is the root-mean-square statistic (RMST) or Hellinger divergence, as proposed by Perkins et al. [1, 2]. Hellinger divergence (HD) is computed as proposed in [3].

Usage

bootstrap2x2(x, stat = "rmst", num.permut = 100)

Arguments

Details

For goodness-of-fit the following null hypothesis is tested H_θ: p = p(θ) To conduct a single simulation, we perform the following three-step procedure [1,2]:

1. To generate m i.i.d. draws according to the model distribution p(θ), where θ' is the estimate calculated from the experimental data,

2. To estimate the parameter θ from the data generated in Step 1, obtaining a new estimate θest.

3. To calculate the statistic under consideration (HD, RMST), using the data generated in Step 1 and taking the model distribution to be θest, where θest is the estimate calculated in Step 2 from the data generated in Step 1.

After conducting many such simulations, the confidence level for rejecting the null hypothesis is the fraction of the statistics calculated in step 3 that are less than the statistic calculated from the empirical data. The significance level α is the same as a confidence level of 1-α.

Value

A p-value probability

References

1. Perkins W, Tygert M, Ward R. Chi^2 and Classical Exact Tests Often Wildly Misreport Significance; the Remedy Lies in Computers [Internet]. Uploaded to ArXiv. 2011. Report No.: arXiv:1108.4126v2.

2. Perkins, W., Tygert, M. & Ward, R. Computing the confidence levels or a root-mean square test of goodness-of-fit. 217, 9072-9084 (2011).

3. Basu, A., Mandal, A. & Pardo, L. Hypothesis testing for two discrete populations based on the Hellinger distance. Stat. Probab. Lett. 80, 206-214 (2010).

Examples

    set.seed(123)
    TeaTasting = matrix(c(8, 350, 2, 20), nrow = 2,
                        dimnames = list(Guess = c("Milk", "Tea"),
                        Truth = c("Milk", "Tea")))
    ## Small num.permut for test's speed sake
    bootstrap2x2( TeaTasting, stat = "all", num.permut = 100 )